Wednesday, February 25, 2009

Intuition and Nonlinearity!!!

I gave a midterm exam to my PhD class today, and accidentally, more carefully observed their problem solving methods. Roughly speaking, I can divide students into three groups:

Most linear: They started from the first question and went to the last. Not much variation in the linear path.

Intermediate: They focused on one question for a while to solve it and then went to another, but not in a linear way (jumped from 3 to 1, for example). Inside each problem they followed a linear path.

Most non-linear: They jumped inside problems and outside. Some finished part of a problem and moved to another. An extreme case was a student who sometimes worked a problem out of order (came up with the answer, intuitively, first before going through the math to show it).

Also I can divide the students into two groups based on their math background and intuition:

Those with strong math backgroun but realtively weak intuition (plausibly not much economic background).

Interesting observation: There was a positive correlation between the two measures. That is more technically trained students tend to be more linear, on average (not always, of course).

I have been dealing with this issue in my professional life for quite a while: I have very good math and technical background, how I can develop more intuition. What I learned from "Nihil Nimus" book was a big help. My observation today is another piece of this puzzle. If I am right, to improve intuition I should try to think and work less linearly.

These are mostly conjectures based on limited observations. If you have your own, please write it in the comments!